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Fermat and Mersenne numbers in $k$-Pell sequence

Математичні Студії, 2021
For an integer $k\geq 2$, let $(P_n^{(k)})_{n\geq 2-k}$ be the $k$-generalized Pell sequence, which starts with $0,\ldots,0,1$ ($k$ terms) and each term afterwards is defined by the recurrence $ P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}
B. Normenyo, S. Rihane, A. Togbe
doaj   +3 more sources

Features of digital signal processing algorithms using Galois fields GF(2n+1). [PDF]

PLoS ONE, 2023
An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1 ...
Ibragim E Suleimenov, Yelizaveta S Vitulyova, Dinara K Matrassulova   +2 more
doaj   +2 more sources

On Mersenne Numbers and their Bihyperbolic Generalizations [PDF]

Annales Mathematicae Silesianae
In this paper, we introduce Mersenne and Mersenne–Lucas bihyperbolic numbers, i.e. bihyperbolic numbers whose coefficients are consecutive Mersenne and Mersenne–Lucas numbers.
Bród Dorota, Szynal-Liana Anetta
doaj   +2 more sources

Learned pseudo-random number generator: WGAN-GP for generating statistically robust random numbers. [PDF]

PLoS ONE, 2023
Pseudo-random number generators (PRNGs) are software algorithms generating a sequence of numbers approximating the properties of random numbers. They are critical components in many information systems that require unpredictable and nonarbitrary ...
Kiyoshiro Okada, Katsuhiro Endo, Kenji Yasuoka, Shuichi Kurabayashi   +3 more
doaj   +2 more sources

Generalised Mersenne numbers revisited [PDF]

, 2013
Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography.
Robert Granger, Andrew Moss
openalex   +7 more sources

Partitions of numbers and the algebraic principle of Mersenne, Fermat and even perfect numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Let ρ be an odd prime greater than or equal to 11. In a previous work, starting from an M-cycle in a finite field 𝔽_ρ, it has been established how the divisors of Mersenne, Fermat and Lehmer numbers arise.
A. M. S. Ramasamy
doaj   +2 more sources

Exponential sums over Mersenne numbers [PDF]

, 2003
© Foundation Compositio Mathematica 2004. Cambridge Journals. doi: 10.1112/S0010437X03000022.We give estimates for exponential sums of the form Σn≤N Λ(n) exp(2πiagn/m), where m is a positive integer, a and g are integers relatively prime to m, and Λ is ...
William D. Banks, Alessandro Conflitti, John Friedlander, Igor E. Shparlinski   +3 more
openalex   +3 more sources

BiEntropy, TriEntropy and Primality [PDF]

Entropy, 2020
The order and disorder of binary representations of the natural numbers < 28 is measured using the BiEntropy function. Significant differences are detected between the primes and the non-primes.
Grenville J. Croll
doaj   +2 more sources

Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, II [PDF]

Notes on Number Theory and Discrete Mathematics
Let ρ be an odd prime ≥ 11. In Part I, starting from an M-cycle in a finite field 𝔽_ρ, we have established how the divisors of Mersenne, Fermat and Lehmer numbers arise.
A. M. S. Ramasamy
doaj   +2 more sources

Overpseudoprimes, and Mersenne and Fermat numbers as primover numbers [PDF]

, 2012
We introduce a new class of pseudoprimes-so called "overpseudoprimes to base $b$", which is a subclass of strong pseudoprimes to base $b$. Denoting via $|b|_n$ the multiplicative order of $b$ modulo $n$, we show that a composite $n$ is overpseudoprime if
Vladimir Shevelev, Gilberto García-Pulgarín, Juan Miguel Velásquez-Soto, John H. Castillo   +3 more
openalex   +5 more sources